In this Appendix we derive expression for the level of temperature fluctuations \(\left\langle \theta ^{2} \right\rangle \) , density fluctuations \(\left\langle \rho ^{\prime \, 2} \right\rangle \) 
as well as temperature–density correlations \(\left\langle \theta \, \rho ^{\prime }\right\rangle \) 
using the method described by [1]}, [2]}, [3]}.
Evolution of temperature field \(T(t,{r})\)  in
a compressible fluid velocity field \({\bf U}(t,{r})\)  is given by [4]}
\({\partial T \over \partial t} + ({\bf U} \cdot {\nabla })T + (\gamma - 1) T ({\nabla } \cdot {U}) = D \Delta T + J_\nu ,\) 
